Optical system

Abstract

where f is a focal length of the optical system, i is an order of each of the plurality of lenses counted from an enlargement side, Ri1 and Ri2 are curvature radii of lens surfaces of an i-th lens at the enlargement side and a reduction side in a cross section including an optical axis, respectively, Ni and νi are a refractive index and an Abbe number of the i-th lens, respectively, φi1=(Ni−1)/Ri1, and φi2=(1−Ni)/Ri2.

What is claimed is: 
     
         1 . An optical system comprising a plurality of lenses, wherein the following conditional expression is satisfied: 
       
         
           
             
               
                 | 
                 
                   
                     
                       Σ 
                       i 
                     
                      
                     
                       1 
                       
                         
                           υ 
                           i 
                         
                          
                         
                           N 
                           i 
                           2 
                         
                       
                     
                      
                     
                       ( 
                       
                         
                           φ 
                           
                             i 
                              
                             
                               1 
                               + 
                             
                           
                         
                          
                         
                           φ 
                           
                             i 
                              
                             2 
                           
                         
                       
                       ) 
                     
                   
                   f 
                 
                 | 
                 
                   ≤ 
                   
                     3 
                     × 
                     1 
                      
                     
                       0 
                       
                         - 
                         3 
                       
                     
                   
                 
               
               , 
             
           
         
         where f is a focal length of the optical system, i is an order of each of the plurality of lenses counted from an enlargement side, R i1  and R i2  are curvature radii of lens surfaces of an i-th lens at the enlargement side and a reduction side in a cross section including an optical axis, respectively, N i  and ν i  are a refractive index and an Abbe number of the i-th lens, respectively, φ i1 =(N i −1)/R i1 , and φ i2 =(1−N i )/R i2 . 
       
     
     
         2 . The optical system according to  claim 1 , wherein the following conditional expression is satisfied:
   8.3≤ L/f≤ 12.5,
   where L is a distance on the optical axis from a focal point of the optical system at the enlargement side to a reducing plane.   
     
     
         3 . The optical system according to  claim 1 , wherein
 the plurality of lenses includes one or more negative lenses and one or more positive lenses, and   the following conditional expressions are satisfied:
   35≤ν n , and
 
   25≤ν p −ν n ,
 
   where ν n  is an Abbe number of the negative lens having a smallest Abbe number among the one or more negative lenses, and ν p  is an Abbe number of the positive lens having a largest Abbe number among the one or more positive lenses.   
     
     
         4 . The optical system according to  claim 1 , wherein at least one of the plurality of lenses includes an aspheric surface that is rotationally asymmetric about the optical axis. 
     
     
         5 . The optical system according to  claim 4 , wherein the lens including the aspheric surface is made of a resin. 
     
     
         6 . The optical system according to  claim 4 , wherein the lens disposed closest to the reduction side among the plurality of lenses includes the aspheric surface. 
     
     
         7 . The optical system according to  claim 1 , wherein the plurality of lenses includes a positive lens, a negative lens, a positive lens, and a positive lens disposed in this order from the enlargement side. 
     
     
         8 . The optical system according to  claim 1 , wherein the plurality of lenses includes a negative lens, a positive lens, a negative lens, a positive lens, and a negative lens disposed in this order from the enlargement side. 
     
     
         9 . The optical system according to  claim 1 , wherein the plurality of lenses includes a positive lens, a negative lens, a positive lens, a positive lens, and a positive lens disposed in this order from the enlargement side. 
     
     
         10 . The optical system according to  claim 1 , wherein an aperture stop is disposed between a positive lens and a negative lens included in the plurality of lenses, the positive lens being disposed closest to the enlargement side among the plurality of lenses, the negative lens being disposed adjacent to a reduction side of the positive lens. 
     
     
         11 . The optical system according to  claim 1 , wherein the lens surface at the enlargement side of the lens disposed closest to the enlargement side among the plurality of lenses has a convex shape toward the enlargement side. 
     
     
         12 . The optical system according to  claim 1 , wherein the lens surface at the reduction side of the lens disposed closest to the reduction side among the plurality of lenses has a convex shape toward the reduction side. 
     
     
         13 . An image reading apparatus comprising:
 the optical system according to  claim 1 ; and   a light receiving unit that receives a light flux from an object condensed by the optical system.